This thesis concerns the effect of rounding on statistical procedures, where rounding is taken to be the grouping of data at the midpoints of equally spaced intervals. The characteristic function of the rounded distribution is obtained. This is used to derive general expressions for the moments of univariate and bivariate distributions that have been subject to rounding. The interactive effect of rounding and skewness on the moments is examined. The performance of certain normal test statistics is examined for rounded data. A study is carried out to obtain precise values for the significance level and power of these statistical tests for rounded data, over many distributions. Guidance is given on what is an appropriate degree of precision for normal data. Special consideration is given to how much non-normality can be allowed without the effect of rounding seriously distorting the significance level and power of a test. Standard methods of estimating the parameters of a distribution are compared with respect to loss in information caused by rounding. Normal, gamma and exponential distributions are examined. Computational methods are presented for computing the maximum likelihood estimates from rounded normal and gamma data. In general it is concluded that the effect of rounding on statistical procedures can be increased by the departure from normality of the population. It was found that less precision is required of the recorded data than that which is usually given.